Key points are not available for this paper at this time.
Given two irreducible conics C and D over a finite field Fq with q odd, we show that there are q²/4+O (q^3/2) points P in P² (Fq) such that P is external to C and internal to D. This answers a question of Korchm\'aros. We also prove the analogous result for higher-dimensional smooth quadric hypersurfaces over P^n-1 with n odd, where the answer is q^n-1/4+O (q^n-3{2}).
Asgarli et al. (2024) studied this question.